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It can meet the vertical calibration operation requirements of mobile phones before contact Angle measurement.</p></li><li><p><a href="./drop-pic-process.html"><strong>Droplet Photo Processing</strong></a>. It can meet all kinds of processing requirements for images after contact Angle measurement and obtain the final contact Angle data.</p></li></ol></div><nav class="table-of-contents"><ul><li><a href="#_1-overview-of-contact-angle">1. Overview of Contact Angle</a></li><li><a href="#_2-vertical-calibration-of-equipment">2. Vertical calibration of equipment</a></li><li><a href="#_3-droplet-photo-processing">3. Droplet photo processing</a><ul><li><a href="#_3-1-read-images-upload-images">3.1 Read images / Upload images</a></li><li><a href="#_3-2-crop-the-picture-to-the-appropriate-size">3.2 Crop the picture to the appropriate size</a></li><li><a href="#_3-3-search-for-the-best-outline-of-the-droplet">3.3 Search for the best outline of the droplet</a></li><li><a href="#_3-4-search-for-the-baseline">3.4 Search for the baseline</a></li><li><a href="#_3-5-calculate-the-contact-angle">3.5 Calculate the contact Angle</a></li></ul></li><li><a href="#_4-other-content-expansion">4. Other content expansion</a><ul><li><a href="#_4-1-imagej">4.1 ImageJ</a></li><li><a href="#_4-2-algorithm">4.2 Algorithm</a></li></ul></li></ul></nav><h2 id="_1-overview-of-contact-angle" tabindex="-1">1. Overview of Contact Angle <a class="header-anchor" href="#_1-overview-of-contact-angle" aria-label="Permalink to &quot;1.  Overview of Contact Angle&quot;">​</a></h2><p>The surface tension property of a liquid on a solid is generally described by the surface wetting performance of the solid. The most easily measurable and quantifiable wetting performance parameter is the <strong>contact angle</strong>: The contact angle is the angle (<mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container>) between the gas - liquid interface and the solid - liquid interface when the liquid droplet is in equilibrium on the solid surface, as shown in Figure 1:</p><p><img src="/phys-chem/assets/%E5%9B%BE1.dzflNXkZ.png" alt="图1" loading="lazy"><span class="center"><strong><!--[-->Figure 1 Definition diagram of the contact Angle<!--]--></strong></span></p><p>In figure 1, <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.669ex;" xmlns="http://www.w3.org/2000/svg" width="2.91ex" height="1.644ex" role="img" focusable="false" viewBox="0 -431 1286.2 726.7" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z" style="stroke-width:3;"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(394,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sg</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> for solid - gas interfacial tension, <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.669ex;" xmlns="http://www.w3.org/2000/svg" width="2.724ex" height="1.644ex" role="img" focusable="false" viewBox="0 -431 1204.1 726.7" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z" style="stroke-width:3;"></path><path data-c="67" d="M329 409Q373 453 429 453Q459 453 472 434T485 396Q485 382 476 371T449 360Q416 360 412 390Q410 404 415 411Q415 412 416 414V415Q388 412 363 393Q355 388 355 386Q355 385 359 381T368 369T379 351T388 325T392 292Q392 230 343 187T222 143Q172 143 123 171Q112 153 112 133Q112 98 138 81Q147 75 155 75T227 73Q311 72 335 67Q396 58 431 26Q470 -13 470 -72Q470 -139 392 -175Q332 -206 250 -206Q167 -206 107 -175Q29 -140 29 -75Q29 -39 50 -15T92 18L103 24Q67 55 67 108Q67 155 96 193Q52 237 52 292Q52 355 102 398T223 442Q274 442 318 416L329 409ZM299 343Q294 371 273 387T221 404Q192 404 171 388T145 343Q142 326 142 292Q142 248 149 227T179 192Q196 182 222 182Q244 182 260 189T283 207T294 227T299 242Q302 258 302 292T299 343ZM403 -75Q403 -50 389 -34T348 -11T299 -2T245 0H218Q151 0 138 -6Q118 -15 107 -34T95 -74Q95 -84 101 -97T122 -127T170 -155T250 -167Q319 -167 361 -139T403 -75Z" transform="translate(278,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">lg</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> for liquid - gas interfacial tension, <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.357ex;" xmlns="http://www.w3.org/2000/svg" width="2.555ex" height="1.332ex" role="img" focusable="false" viewBox="0 -431 1129.2 588.8" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z" style="stroke-width:3;"></path><path data-c="6C" d="M42 46H56Q95 46 103 60V68Q103 77 103 91T103 124T104 167T104 217T104 272T104 329Q104 366 104 407T104 482T104 542T103 586T103 603Q100 622 89 628T44 637H26V660Q26 683 28 683L38 684Q48 685 67 686T104 688Q121 689 141 690T171 693T182 694H185V379Q185 62 186 60Q190 52 198 49Q219 46 247 46H263V0H255L232 1Q209 2 183 2T145 3T107 3T57 1L34 0H26V46H42Z" transform="translate(394,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sl</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> represents the interfacial tension between solid and liquid, and <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container> is the contact angle. Obviously, when the droplet is in equilibrium, it satisfies equation (1):</p><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" width="full" style="direction:ltr;text-align:center;margin:1em 0;display:flex;min-width:29.474ex;position:relative;"><svg style="overflow:visible;min-height:1px;vertical-align:-0.617ex;min-width:29.474ex;" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.366ex" role="img" focusable="false" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -772.8)"><g data-mml-node="math"><g data-mml-node="mtable" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 772.8) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="4435.8 -772.8 1 1045.7" style="overflow:visible;"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,22.8)"><g data-mml-node="mtd"><g 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transform="translate(0,772.8)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-750)"><g data-mml-node="mtext"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z" style="stroke-width:3;"></path><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z" transform="translate(389,0)" style="stroke-width:3;"></path><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z" transform="translate(889,0)" style="stroke-width:3;"></path></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;overflow:hidden;width:100%;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(1)</mtext></mtd><mtd><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">lg</mi></mrow></msub><mo>⋅</mo><mi>cos</mi><mo data-mjx-texclass="NONE">⁡</mo><mrow data-mjx-texclass="ORD"><mi>θ</mi></mrow><mo>+</mo><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sl</mi></mrow></msub><mo>=</mo><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sg</mi></mrow></msub></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container><p>equation (1) is the Young equation, also known as the wetting formula. Furthermore, it can be obtained that:</p><mjx-container tabindex="0" class="MathJax" jax="SVG" display="true" width="full" style="direction:ltr;text-align:center;margin:1em 0;display:flex;min-width:26.111ex;position:relative;"><svg style="overflow:visible;min-height:1px;vertical-align:-2.059ex;min-width:26.111ex;" xmlns="http://www.w3.org/2000/svg" width="100%" height="5.25ex" role="img" focusable="false" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1410.2)"><g data-mml-node="math"><g data-mml-node="mtable" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 1410.2) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="3692.5 -1410.2 1 2320.3" style="overflow:visible;"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,71.5)"><g data-mml-node="mtd"><g data-mml-node="mi"><path data-c="63" d="M370 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transform="translate(889,0)" style="stroke-width:3;"></path></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;overflow:hidden;width:100%;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd><mtext>(2)</mtext></mtd><mtd><mi>cos</mi><mo data-mjx-texclass="NONE">⁡</mo><mrow data-mjx-texclass="ORD"><mi>θ</mi></mrow><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sg</mi></mrow></msub><mo>−</mo><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">sl</mi></mrow></msub></mrow><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">lg</mi></mrow></msub></mfrac></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container><p>When 0° &lt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container> &lt; 90°, 1 &gt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="4.465ex" height="1.62ex" role="img" focusable="false" viewBox="0 -705 1973.7 716" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" style="stroke-width:3;"></path><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z" transform="translate(444,0)" style="stroke-width:3;"></path><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z" transform="translate(944,0)" style="stroke-width:3;"></path></g><g data-mml-node="mo" transform="translate(1338,0)"><path data-c="2061" d="" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1504.7,0)"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo data-mjx-texclass="NONE">⁡</mo><mrow data-mjx-texclass="ORD"><mi>θ</mi></mrow></math></mjx-assistive-mml></mjx-container> &gt; 0, the <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.375ex;" xmlns="http://www.w3.org/2000/svg" width="3.569ex" height="1.35ex" role="img" focusable="false" viewBox="0 -431 1577.5 596.6" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z" style="stroke-width:3;"></path><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z" transform="translate(556,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">SV</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> &gt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.375ex;" xmlns="http://www.w3.org/2000/svg" width="3.369ex" height="1.35ex" role="img" focusable="false" viewBox="0 -431 1489.1 596.6" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z" style="stroke-width:3;"></path><path data-c="4C" d="M128 622Q121 629 117 631T101 634T58 637H25V683H36Q48 680 182 680Q324 680 348 683H360V637H333Q273 637 258 635T233 622L232 342V129Q232 57 237 52Q243 47 313 47Q384 47 410 53Q470 70 498 110T536 221Q536 226 537 238T540 261T542 272T562 273H582V268Q580 265 568 137T554 5V0H25V46H58Q100 47 109 49T128 61V622Z" transform="translate(556,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">SL</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>. Solid surfaces tend to be wetted by liquids.</p><p>When 90° &lt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container> &lt; 180°, 0 &gt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.025ex;" xmlns="http://www.w3.org/2000/svg" width="4.465ex" height="1.62ex" role="img" focusable="false" viewBox="0 -705 1973.7 716" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 404Q281 408 258 408Q209 408 178 376Q131 329 131 219Q131 137 162 90Q203 29 272 29Q313 29 338 55T374 117Q376 125 379 127T395 129H409Q415 123 415 120Q415 116 411 104T395 71T366 33T318 2T249 -11Q163 -11 99 53T34 214Q34 318 99 383T250 448T370 421T404 357Q404 334 387 320Z" style="stroke-width:3;"></path><path data-c="6F" d="M28 214Q28 309 93 378T250 448Q340 448 405 380T471 215Q471 120 407 55T250 -10Q153 -10 91 57T28 214ZM250 30Q372 30 372 193V225V250Q372 272 371 288T364 326T348 362T317 390T268 410Q263 411 252 411Q222 411 195 399Q152 377 139 338T126 246V226Q126 130 145 91Q177 30 250 30Z" transform="translate(444,0)" style="stroke-width:3;"></path><path data-c="73" d="M295 316Q295 356 268 385T190 414Q154 414 128 401Q98 382 98 349Q97 344 98 336T114 312T157 287Q175 282 201 278T245 269T277 256Q294 248 310 236T342 195T359 133Q359 71 321 31T198 -10H190Q138 -10 94 26L86 19L77 10Q71 4 65 -1L54 -11H46H42Q39 -11 33 -5V74V132Q33 153 35 157T45 162H54Q66 162 70 158T75 146T82 119T101 77Q136 26 198 26Q295 26 295 104Q295 133 277 151Q257 175 194 187T111 210Q75 227 54 256T33 318Q33 357 50 384T93 424T143 442T187 447H198Q238 447 268 432L283 424L292 431Q302 440 314 448H322H326Q329 448 335 442V310L329 304H301Q295 310 295 316Z" transform="translate(944,0)" style="stroke-width:3;"></path></g><g data-mml-node="mo" transform="translate(1338,0)"><path data-c="2061" d="" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1504.7,0)"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo data-mjx-texclass="NONE">⁡</mo><mrow data-mjx-texclass="ORD"><mi>θ</mi></mrow></math></mjx-assistive-mml></mjx-container> &gt; -1, the <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.375ex;" xmlns="http://www.w3.org/2000/svg" width="3.569ex" height="1.35ex" role="img" focusable="false" viewBox="0 -431 1577.5 596.6" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z" style="stroke-width:3;"></path><path data-c="56" d="M114 620Q113 621 110 624T107 627T103 630T98 632T91 634T80 635T67 636T48 637H19V683H28Q46 680 152 680Q273 680 294 683H305V637H284Q223 634 223 620Q223 618 313 372T404 126L490 358Q575 588 575 597Q575 616 554 626T508 637H503V683H512Q527 680 627 680Q718 680 724 683H730V637H723Q648 637 627 596Q627 595 515 291T401 -14Q396 -22 382 -22H374H367Q353 -22 348 -14Q346 -12 231 303Q114 617 114 620Z" transform="translate(556,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">SV</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> &lt; <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.375ex;" xmlns="http://www.w3.org/2000/svg" width="3.369ex" height="1.35ex" role="img" focusable="false" viewBox="0 -431 1489.1 596.6" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D70E" d="M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z" style="stroke-width:3;"></path></g><g data-mml-node="TeXAtom" transform="translate(604,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="53" d="M55 507Q55 590 112 647T243 704H257Q342 704 405 641L426 672Q431 679 436 687T446 700L449 704Q450 704 453 704T459 705H463Q466 705 472 699V462L466 456H448Q437 456 435 459T430 479Q413 605 329 646Q292 662 254 662Q201 662 168 626T135 542Q135 508 152 480T200 435Q210 431 286 412T370 389Q427 367 463 314T500 191Q500 110 448 45T301 -21Q245 -21 201 -4T140 27L122 41Q118 36 107 21T87 -7T78 -21Q76 -22 68 -22H64Q61 -22 55 -16V101Q55 220 56 222Q58 227 76 227H89Q95 221 95 214Q95 182 105 151T139 90T205 42T305 24Q352 24 386 62T420 155Q420 198 398 233T340 281Q284 295 266 300Q261 301 239 306T206 314T174 325T141 343T112 367T85 402Q55 451 55 507Z" style="stroke-width:3;"></path><path data-c="4C" d="M128 622Q121 629 117 631T101 634T58 637H25V683H36Q48 680 182 680Q324 680 348 683H360V637H333Q273 637 258 635T233 622L232 342V129Q232 57 237 52Q243 47 313 47Q384 47 410 53Q470 70 498 110T536 221Q536 226 537 238T540 261T542 272T562 273H582V268Q580 265 568 137T554 5V0H25V46H58Q100 47 109 49T128 61V622Z" transform="translate(556,0)" style="stroke-width:3;"></path></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false">SL</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>. Solid surfaces tend not to be wetted by liquids.</p><p>Therefore, when discussing the wettability of a liquid on a solid surface, a 90° contact Angle is generally used as the criterion for whether it wets or not: <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container> &gt; 90° indicates non-wettability, and <mjx-container class="MathJax" jax="SVG" style="direction:ltr;position:relative;"><svg style="overflow:visible;min-height:1px;min-width:1px;vertical-align:-0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.618ex" role="img" focusable="false" viewBox="0 -705 469 715" aria-hidden="true"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z" style="stroke-width:3;"></path></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline" style="top:0px;left:0px;clip:rect(1px, 1px, 1px, 1px);-webkit-touch-callout:none;-webkit-user-select:none;-khtml-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;position:absolute;padding:1px 0px 0px 0px;border:0px;display:block;width:auto;overflow:hidden;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></mjx-assistive-mml></mjx-container> &lt; 90° indicates wettability.</p><p>Due to the universality and ease of use of contact Angle measurement, it can be said that contact Angle has become one of the most important parameters for characterizing the surface tension properties of liquids on solids, and contact Angle measurement operations have also become one of the de facto standards for characterizing surface wettability. Meanwhile, through the measurement of the contact Angle, the critical micelle concentration data of the surfactant can also be calculated.</p><h2 id="_2-vertical-calibration-of-equipment" tabindex="-1">2. Vertical calibration of equipment <a class="header-anchor" href="#_2-vertical-calibration-of-equipment" aria-label="Permalink to &quot;2.  Vertical calibration of equipment&quot;">​</a></h2><p><a href="./vertical-calibration.html"><strong>Link to the vertical calibration function of the equipment</strong></a></p><p>This function is relatively simple. After clicking &quot;Call Sensor&quot;, you can use the phone&#39;s own sensor to perform necessary vertical calibration operations on the phone.</p><p>The vast majority of mobile phones have both <strong>gravity sensing</strong> and <strong>direction sensing</strong> implementations. Therefore, this function briefly explains the advantages and disadvantages of these two implementations and provides operation suggestions. Typical explanations and suggestions are as follows:</p><p><img src="/phys-chem/assets/%E5%9E%82%E7%9B%B4%E6%A0%A1%E5%87%86%E8%AF%B4%E6%98%8E1.BBxL6nx1.jpg" alt="垂直校准说明1" loading="lazy"></p><p>When using this function, the typical data information interface is as follows:</p><p><img src="/phys-chem/assets/%E5%9E%82%E7%9B%B4%E6%A0%A1%E5%87%86%E8%AF%B4%E6%98%8E2.BW24JQrt.jpg" alt="垂直校准说明2" loading="lazy"></p><p>After calibration is completed, you can return to the previous page or jump to another page to exit the vertical calibration. You can also click the &quot;End Calibration&quot; button to temporarily exit the calibration.</p><h2 id="_3-droplet-photo-processing" tabindex="-1">3. Droplet photo processing <a class="header-anchor" href="#_3-droplet-photo-processing" aria-label="Permalink to &quot;3.  Droplet photo processing&quot;">​</a></h2><p><a href="./drop-pic-process.html"><strong>Link to droplet photo processing function</strong></a></p><p>The droplet photo processing function mainly consists of the following steps:</p><h3 id="_3-1-read-images-upload-images" tabindex="-1">3.1 Read images / Upload images <a class="header-anchor" href="#_3-1-read-images-upload-images" aria-label="Permalink to &quot;3.1 Read images / Upload images&quot;">​</a></h3><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E1.DCABER9r.jpg" alt="液滴照片处理说明1" loading="lazy"></p><p>After clicking to read the image, the software will automatically perform grayscale processing on the image. And draw a grayscale image for the next step of operation.</p><div class="info custom-block github-alert"><p class="custom-block-title">Tips：</p><p></p><p>After uploading the picture, you can click this button to re-upload the picture (as shown in the following picture).</p><p>Therefore, it is possible to continuously process multiple images without refreshing the page.</p></div><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E2.D0b6WpMP.jpg" alt="液滴照片处理说明2" loading="lazy"></p><h3 id="_3-2-crop-the-picture-to-the-appropriate-size" tabindex="-1">3.2 Crop the picture to the appropriate size <a class="header-anchor" href="#_3-2-crop-the-picture-to-the-appropriate-size" aria-label="Permalink to &quot;3.2 Crop the picture to the appropriate size&quot;">​</a></h3><p>This step is mainly completed by clicking on the grayscale image. The specific operation functions include: short press to control the expansion/reduction of the border in the cropping area; Long press to clear the existing selection box.</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E3.CH-J0tfh.jpg" alt="液滴照片处理说明3" loading="lazy"></p><div class="info custom-block github-alert"><p class="custom-block-title">Tips：</p><p></p><p>You can click the &quot;Crop&quot; button <strong>repeatedly</strong>. It is recommended to crop photos in small quantities multiple times, which can greatly simplify the cropping process.</p></div><p>A typical recommended cutting size is shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E4.Ddp_jF0w.jpg" alt="液滴照片处理说明4" loading="lazy"></p><p>After obtaining a relatively ideal cropping result, select the most ideal red box to be cropped, click the &quot;Finish Cropping&quot; button to end the cropping, and proceed to the next step.</p><h3 id="_3-3-search-for-the-best-outline-of-the-droplet" tabindex="-1">3.3 Search for the best outline of the droplet <a class="header-anchor" href="#_3-3-search-for-the-best-outline-of-the-droplet" aria-label="Permalink to &quot;3.3 Search for the best outline of the droplet&quot;">​</a></h3><p>This step mainly involves adjusting the slide rail to modify the parameters of the contour search algorithm in real time and to view the contour effect in real time.</p><p>In particular, when there are many &quot;misidentified contour lines&quot;, the misidentified contour lines can be manually filtered through the &quot;side mask&quot; and &quot;center Mask&quot; functions.</p><h4 id="_3-3-1-contour-edge-detection" tabindex="-1">3.3.1 Contour / Edge detection <a class="header-anchor" href="#_3-3-1-contour-edge-detection" aria-label="Permalink to &quot;3.3.1 Contour / Edge detection&quot;">​</a></h4><p>This application offers two edge detection methods (<a href="https://docs.opencv.ac.cn/4.12.0/d7/de1/tutorial_js_canny.html" target="_blank" rel="noreferrer"><strong>Canny Algorithm</strong></a> and <a href="https://docs.opencv.ac.cn/4.12.0/d7/dd0/tutorial_js_thresholding.html" target="_blank" rel="noreferrer"><strong>Thresholding Method</strong></a>) to find contours. The detection method switch is located at the top of the image. And a simple description of this algorithm is attached above the switch, as shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E5.D1CVRudM.jpg" alt="液滴照片处理说明5" loading="lazy"></p><p>Of the two algorithms, the Canny algorithm has two parameters (hence two sliders are provided below the image), while the thresholding method has one parameter (hence one slider is provided below the image). To facilitate fine-tuning of parameters, this software provides a &quot;Switch Fine adjustment/Switch coarse adjustment&quot; button. After switching, the range value of the slide rail can be refined/coarsely adjusted. The slide rail and the fine adjustment/fine-tuning switch button are shown in the following figure.</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E6.DyKImv57.jpg" alt="液滴照片处理说明6" loading="lazy"></p><p>Adjusting the slide rail allows you to view the contour effect in real time (superimposing the contour line on the grayscale image). The ideal contour effect is as shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E7.DYqmIjpb.jpg" alt="液滴照片处理说明7" loading="lazy"></p><p>In most cases, there will be a bright area in the middle of the captured droplet that is similar in shape to the light source. This is because the droplet surface projects the shape of the light source behind the droplet through the droplet onto the center of the image.</p><p>This optical phenomenon is extremely common under strong light sources and high contrast conditions.</p><p>In this case, the bright area in the middle of the droplet will inevitably be misidentified as a contour by the contour search algorithm. <strong>At this point, the slide rail should be adjusted as much as possible while ensuring that the contour of the droplet can be identified as accurately as possible, so as to minimize the misidentification of the contour line in the middle of the droplet.</strong> In this case, the typical contour recognition effect that is more recommended is shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E8.DIGPhMU3.jpg" alt="液滴照片处理说明8" loading="lazy"></p><p>To address the issue of misrecognized contours in the middle of the droplet, this software independently designs an &quot;iterative filtering algorithm&quot;: when the middle contour line is significantly less than the external true contour line, the iterative filtering algorithm of this software will automatically filter out the misrecognized contour line in the middle.</p><p>Of course, there are also situations where parameter tuning cannot filter out misrecognized contour lines. In such cases, the following &quot;mask&quot; function can be used to manually filter out misrecognized contour lines.</p><h4 id="_3-3-2-mask" tabindex="-1">3.3.2 Mask <a class="header-anchor" href="#_3-3-2-mask" aria-label="Permalink to &quot;3.3.2 Mask&quot;">​</a></h4><p>This application provides three masking methods: <strong>side masking</strong>, <strong>baseline masking</strong>, and <strong>center masking</strong>. The mask toggle switch and the mask function introduction are both located at the top of the picture. As shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E8-2.CUe8o3JW.jpg" alt="alt text" loading="lazy"></p><p>When the light transmittance of a solid substrate is poor, the outline of the solid substrate may also be mistakenly identified as the outline of a droplet. At this point, you can use the &quot;<strong>Side Mask</strong>&quot; function. Click on the left or right part of the picture to set the mask and cover the contour lines that are mistakenly recognized on the solid base. The masked contour points will not participate in the subsequent fitting. <strong>This step does not need to pursue extreme precision, as the iterative filtering algorithm of this software can automatically filter out a small number of unmasked misidentified solid substrate lines</strong>. A typical situation of this kind is shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E9.DYjO5zLP.jpg" alt="液滴照片处理说明9" loading="lazy"></p><p>Similarly, when the &quot;misidentified contour lines&quot; in the middle cannot be cleared through parameter adjustment, the &quot;<strong>Center Mask</strong>&quot; function can be used to manually filter out the misidentified contour lines. The interaction logic of the center mask is similar to that of image cropping and will not be elaborated here. A typical situation of this kind is shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E9-2.CbRPn02l.jpg" alt="alt text" loading="lazy"></p><p>Similarly, the &quot;<strong>Baseline Mask</strong>&quot; function can be used to manually filter out misidentified baseline contour lines and various misidentified contour lines below the baseline. <strong>This step does not need to pursue extreme precision, as the iterative filtering algorithm of this software can automatically filter out misidentified contours near the mask line</strong>.</p><p>By rationally using the parameter adjustment slide rail and mask functions, the true contour lines can be as many as possible and the misrecognized contour lines can be as few as possible. This can achieve a better contour recognition effect.</p><div class="info custom-block github-alert"><p class="custom-block-title">Tips：</p><p></p><p>Adjust the slide rail as much as possible to minimize the number of misidentified contour lines in the middle of the droplet.</p><p>Adjust the left and right mask areas to cover the misidentified contour lines on the solid substrate (roughly covering most of them is sufficient).</p></div><p>After completing the contour search, you can click the &quot;Confirm Contour&quot; button to achieve the iteration and fitting of the contour. <strong>If the fitting effect is not good, you can click &quot;Go Back to Previous Step&quot; at any time to search for the contour again.</strong></p><h3 id="_3-4-search-for-the-baseline" tabindex="-1">3.4 Search for the baseline <a class="header-anchor" href="#_3-4-search-for-the-baseline" aria-label="Permalink to &quot;3.4 Search for the baseline&quot;">​</a></h3><p>This step will find the baseline of the droplet based on the fitted elliptical contour line obtained in Step 3.</p><p>The typical operation functions and implementation effects are as shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E10.Cn5UWTm8.jpg" alt="液滴照片处理说明10" loading="lazy"></p><p>You can roughly adjust the baseline by directly clicking on the image: Clicking on the left or right side of the image can roughly adjust the left or right intercept of the baseline. Click the middle of the picture to pan the baseline up or down.</p><p>Based on the coarse adjustment, slide the slider at the bottom of the image to fine-tune the left/right intercept of the baseline.</p><p>After determining the intercept of the baseline, click the &quot;Confirm Baseline&quot; button, and the software will automatically calculate the contact Angle.</p><h3 id="_3-5-calculate-the-contact-angle" tabindex="-1">3.5 Calculate the contact Angle <a class="header-anchor" href="#_3-5-calculate-the-contact-angle" aria-label="Permalink to &quot;3.5 Calculate the contact Angle&quot;">​</a></h3><p>The software will automatically calculate the determination coefficient of contour fitting, the values of the left and right contact angles, the average value of the contact angles, and the Deviation of the left and right contact angles.</p><p>After the calculation is completed, this software will inform the user of the average contact Angle data in the form of a pop-up notification. A typical pop-up notification is shown in the following figure:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E11.CqskCcu8.jpg" alt="液滴照片处理说明11" loading="lazy"></p><p>In addition to pop-up notifications, the file name, average antenna value, and relative deviation value will be displayed in table form at the bottom of the page:</p><p><img src="/phys-chem/assets/%E6%B6%B2%E6%BB%B4%E7%85%A7%E7%89%87%E5%A4%84%E7%90%86%E8%AF%B4%E6%98%8E12.BpSKqE6Y.jpg" alt="液滴照片处理说明12" loading="lazy"></p><p>The &quot;Download&quot; button below the table allows you to download the excel table file containing all the data.</p><h2 id="_4-other-content-expansion" tabindex="-1">4. Other content expansion <a class="header-anchor" href="#_4-other-content-expansion" aria-label="Permalink to &quot;4.  Other content expansion&quot;">​</a></h2><h3 id="_4-1-imagej" tabindex="-1">4.1 ImageJ <a class="header-anchor" href="#_4-1-imagej" aria-label="Permalink to &quot;4.1 ImageJ&quot;">​</a></h3><p>ImageJ is an open-source image processing software maintained by the National Institutes of Health (NIH) in the United States. This software is widely used in image analysis in fields such as biology, medicine, and physics. It can be said that ImageJ is the most commonly used image processing software in the scientific research field, without any doubt.</p><p>In the process of developing the contact Angle image processing software for this business, some ideas of the contact Angle plugin in ImageJ were borrowed.</p><p>In addition, ImageJ is equipped with many powerful functions such as image filtering, morphological operations, edge detection, and region extraction. It can meet various business needs such as cell counting and measurement, protein gel analysis, quantitative analysis of tissue sections, and electron microscope image processing, providing great convenience for scientific researchers.</p><p>The official website link of ImageJ: <a href="https://imagej.net/ij/index.html" target="_blank" rel="noreferrer">https://imagej.net/ij/index.html</a></p><h3 id="_4-2-algorithm" tabindex="-1">4.2 Algorithm <a class="header-anchor" href="#_4-2-algorithm" aria-label="Permalink to &quot;4.2 Algorithm&quot;">​</a></h3><p>This business has designed its own algorithm to achieve the iteration and fitting of droplet contours.</p></div></div></main><footer class="VPDocFooter" data-v-e6f2a212 data-v-1bcd8184><!--[--><!--]--><div class="edit-info" data-v-1bcd8184><!----><div class="last-updated" data-v-1bcd8184><p class="VPLastUpdated" data-v-1bcd8184 data-v-1bb0c8a8>Last updated: <time datetime="2025-11-17T03:07:58.000Z" data-v-1bb0c8a8></time></p></div></div><!----></footer><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><footer class="VPFooter" data-v-d8b57b2d data-v-566314d4><div class="container" data-v-566314d4><p class="message" data-v-566314d4>Bug Feedback：<a href='sms:008613611580728'>0086-13611580728 (SI_Cheng-Yun)</p><p class="copyright" data-v-566314d4>Copyright © 2025 SI_Cheng-Yun. 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